Preprints
M.E. Akramov, J.R. Yusupov, M. Ehrhardt, and D.U. Matrasulov, Transparent boundary conditions for the spatially discrete Schrödinger equation: Reflectionless quantum transport in 1D lattices, 2025 (ongoing project)
J.R. Yusupov, D.U. Matrasulov, Entangled quantum states on graphs, 2025 (ongoing project)
Articles in Journals
Q.U. Asadov, K.K. Sabirov, J.R. Yusupov, Kink-antikink soliton solutions of the nonlinear Klein-Gordonequation on branched structures, EPL 153 52002 (2026)
M. Ehrhardt and C. Zheng, Absorbing Boundary Conditions for Variable Potential Schrödinger Equations via Titchmarsh-Weyl Theory, Communications in Computational Physics, 38 (3), 711-728 (2025)
V.A. Derkach, C. Trunk, J.R. Yusupov, D.U. Matrasulov, Transparent boundary conditions for the stationary Schroedinger equation via Weyl-Titchmarsh theory, J. Phys. A: Math. Theor. 58, 345201 (2025)
J.R. Yusupov, M. Ehrhardt, Kh.Sh. Matyokubov and D.U. Matrasulov, Driven transparent quantum graphs, Physica Scripta, 100 (7), 075224 (2025)
M.E. Akramov, J.R. Yusupov, M. Ehrhardt, H. Susanto and D.U. Matrasulov, Transparent PT-symmetric nonlinear networks, Physica Scripta, 100 (4), 045209, (2025)
M. Akramov, C. Trunk, J. Yusupov, D. Matrasulov, Discrete Schrödinger equation on graphs: An effective model for branched quantum lattice. Europhysics Letters 147 (6), 62001, 2024.
M.E. Akramov, J.R. Yusupov, I.N. Askerzade and D.U. Matrasulov, Discrete sine-Gordon equation on metric graphs: A simple model for Josephson junction networks, Physica Scripta, 98 115238 (2023)
M.E. Akramov, J.R. Yusupov, M. Ehrhardt, H. Susanto, D.U. Matrasulov, Transparent boundary conditions for the nonlocal nonlinear Schrödinger equation: A model for reflectionless propagation of PT-symmetric solitons, Physics Letters A, 459, 128611, 2023
J. Matrasulov, K. Sabirov, Fokker–Planck equation on metric graphs, Physica A: Statistical Mechanics and its Applications, 608, 128279 (2022)
https://www.sciencedirect.com/science/article/abs/pii/S0378437122008378?via%3Dihub
K.K. Sabirov, J.R. Yusupov, M.Ehrhardt, D.U.Matrasulov, Transparent boundary conditions for the sine-Gordon equation: Modeling the reflectionless propagation of kink solitons on a line, Physics Letters A, 423, 127822, 2022
https://www.sciencedirect.com/science/article/abs/pii/S0375960121006861?via%3Dihub
Monographs
Ж.Р.Юсупов, Метрические графы с прозрачными узлами: Модель безотражательного транспорта частиц и волн в квантовых сетях. Монография, «DIZAYN MARKET» Ташкент-2024, 162 стр (PDF)
Talks related to the Project
D. Matrasulov, PT-symmetric physics in networks: From quantum transport to soliton propagation, Dynamics Days Central Asia and Caucasus, Astana, Kazakhstan, May 25-28, 2026
J. Yusupov, Tunable quantum transport and soliton propagation in transparent networks, Dynamics Days Central Asia and Caucasus, Astana, Kazakhstan, May 25-28, 2026
J. Yusupov, Driven quantum networks, ICSM-ICQMT-2025, Fethiye, Turkey, April 28, 2025
J. Yusupov, Tunable wave propagation in branched structures, Dynamics Days Central Asia and Caucasus: 21st Century Silk Road for Science and Peace, Samarkand, Uzbekistan, October 1-5, 2024
S. Usanov, Nonlocal nonlinear Schrödinger equation on metric graphs: A model for generation and transport of parity-time-symmetric nonlocal solitons in networks, International Summer School & Conference Evolution Equations, Approximation and Spectral Optimization, Almaty, Kazakhstan, September 16 - 18, 2024
J. Yusupov, Modeling the reflectionless propagation of vector solitons in networks, International Summer School & Conference Evolution Equations, Approximation and Spectral Optimization, Almaty, Kazakhstan, September 16 - 18, 2024
J. Yusupov, Transparent boundary conditions for nonlinear evolution equations in low-dimensional domains, “Quantum Circle” Doppler Institute Seminar, Prague, Czech Republic, July 11, 2023
J. Yusupov, Transparent boundary conditions for the stationary Schrodinger equation on metric graphs, Dynamics Days Central Asia and Caucasus: 21st Century Silk Road for Science and Peace, Bukhara, Uzbekistan, October 1-4, 2023
J. Yusupov, Transparent boundary conditions for nonlinear evolution equations in low-dimensional domains, International Summer School and Conference on Mathematics for the Micro/Nano-World: From soliton dynamics, nonlinear optics to quantum science and technology, Samarkand, Uzbekistan, September 18-22, 2023.
J. Yusupov, Transparent nonlinear networks, International Conference: Dynamics Days Central Asia & Caucasus, Baku, Azerbaijan, September 28-30, 2022.
J. Yusupov, Tunable quantum transport in networks: From transparent to PT-symmetric quantum graphs, Summer school on Modern trends in quantum science and technologies: From quantum materials to quantum information, Baku, Azerbaijan, September 22 - October 02, 2022
J.Yusupov, Transparent boundary conditions in quantum evolution equations: Modeling and design quantum graphs with transparent vertices, “Applied Functional Analysis” group seminar, Institute of Mathematics, Ilmenau, July 4, 2022
D.Matrasulov, Quantum physics on graphs: From basic research to practical applications, Doppler Institute Seminar, Prague, Czech Republic, November 22, 2022